Large-scale city bridge and tunnel network importance rapid sorting method based on hybrid graph attention network

Abstract

The invention discloses a large-scale city bridge and tunnel network importance rapid sorting method based on a mixed graph attention network. The method comprises the following steps: 1, defining a monomer importance index which considers a structure failure probability and economic loss generated in security, society, function and environment dimensions after failure; 2, calculating the total travel volume, total arrival volume and inter-node travel demand of each node of the bridge-tunnel network; 3, realizing initial traffic flow distribution based on a Frank-Wolfe algorithm; 4, possibly invalid edges in the bridge and tunnel network are damaged one by one to generate a redistribution traffic flow making data set; 5, designing a hybrid graph attention network; and 6, training the hybrid graph attention network designed in the step 5, and quickly sorting the importance of the large-scale urban bridge and tunnel network by using the trained hybrid graph attention network. According to the method, the defect of low efficiency caused by repeated solution of a high-dimensional optimization problem in bridge and tunnel network monomer importance index calculation is overcome.

Description

Technical Field

[0001] This invention relates to a method for evaluating the service performance of bridge and tunnel networks, specifically to a method for rapidly ranking the importance of large-scale urban bridge and tunnel networks based on hybrid graph attention networks. Background Technology

[0002] Bridges and tunnels, as lifeline engineering projects of transportation networks, play a vital role in connecting different areas and fulfilling people's needs for convenient and efficient travel. However, as a weak link in the transportation network, bridges and tunnels will inevitably deteriorate due to load, structural defects, and environmental conditions over long-term use, leading to structural damage, casualties, decreased network functionality, and environmental pollution, resulting in significant negative impacts in multiple aspects.

[0003] Under the constraint of limited maintenance funds, scientific planning of fund allocation is crucial. A prerequisite for accomplishing this is quantifying and ranking the importance of individual bridge and tunnel structures at the network level. Importance metrics are used to quantify the importance of different objects in a given system. This can identify system bottlenecks and propose scientific optimization solutions for system improvement or maintenance activities. Currently, the commonly used importance ranking method is a risk-based importance ranking method, which calculates the failure probability of a structure multiplied by the economic losses incurred by the failure. However, the economic losses calculated in a transportation network inevitably include the additional detour distance and time losses caused by the reduction in road capacity due to failure. These are directly related to traffic flow redistribution solutions, and their computational dimensionality increases exponentially with network size; in large-scale networks, the total computation time can even be measured in days.

[0004] Traffic flow redistribution computation essentially involves solving for a specific output given network topology features as input. This involves data-driven characteristics, allowing for rapid computation through deep learning proxy models. Graph neural networks, as deep learning models specifically designed for modeling topology, are feasible for this task. Therefore, this paper proposes a fast importance ranking method for large-scale urban bridge and tunnel networks based on graph neural networks. This method achieves a significant efficiency improvement compared to traditional explicit algorithms, providing substantial support for the intelligent operation and maintenance of bridge and tunnel networks. Summary of the Invention

[0005] To address the time-consuming computation of importance ranking for individual bridge and tunnel networks in current methods, this invention provides a fast ranking method for the importance of large-scale urban bridge and tunnel networks based on hybrid graph attention networks. This method overcomes the inefficiency caused by repeatedly solving high-dimensional optimization problems in the calculation of importance indicators for individual bridge and tunnel networks, achieving accurate and rapid calculation of importance indicators for large-scale urban bridge and tunnel networks, and is suitable for the efficient management and maintenance of such networks.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] A fast importance ranking method for large-scale urban bridge and tunnel networks based on hybrid graph attention networks includes the following steps:

[0008] Step 1: Define an individual importance index that considers the probability of structural failure and the economic losses that will result in safety, society, function, and environment after failure.

[0009] Step 2: Calculate the total number of trips, total number of arrivals, and travel demand between nodes in the bridge-tunnel network;

[0010] Step 3: Implement initial traffic flow assignment based on the Frank-Wolfe algorithm;

[0011] Step 4: Destroy potentially faulty edges in the bridge-tunnel network one by one to generate a dataset of traffic flow redistribution;

[0012] Step 5: Design a hybrid graph attention network to model the topological association patterns between the edge capacity reduction vector and the flow redistribution vector in the bridge-tunnel network;

[0013] Step 6: Train the hybrid graph attention network designed in Step 5, and use the trained hybrid graph attention network to quickly rank the importance of large-scale urban bridge and tunnel networks.

[0014] Compared with the prior art, the present invention has the following advantages:

[0015] 1. To address the time-consuming calculation of importance ranking for individual bridge and tunnel networks in current urban bridge and tunnel network systems, this invention proposes a fast ranking method for the importance of large-scale urban bridge and tunnel networks based on a hybrid graph attention network. This method effectively solves the inefficiency caused by repeatedly solving high-dimensional optimization problems in the current calculation of importance indicators for individual bridge and tunnel networks by designing a hybrid graph attention network that integrates the topological constraints of static adjacency matrices and the learnable correlations of dynamic adjacency matrices. This achieves accurate and fast calculation of importance indicators for large-scale urban bridge and tunnel networks and is suitable for the efficient management and maintenance of large-scale urban bridge and tunnel networks.

[0016] 2. Using a large-scale bridge and tunnel network (containing hundreds of nodes, edges, and individual bridges and tunnels) of a city with a population of ten million as a case study object for training and testing, the invention is demonstrated to be able to accurately and quickly calculate the importance indicators of large-scale urban bridge and tunnel networks, and can provide support for the efficient management and maintenance of large-scale urban bridge and tunnel networks. Attached Figure Description

[0017] Figure 1 This is a flowchart illustrating a fast ranking method for the importance of large-scale urban bridge and tunnel networks based on hybrid graph attention networks.

[0018] Figure 2 This is a topology diagram of the bridge-tunnel network;

[0019] Figure 3 Calculate the error convergence graph for inter-node travel demand;

[0020] Figure 4 Heatmap of travel demand matrix for nodes;

[0021] Figure 5 The objective function descent graph is shown when performing initial traffic flow assignment;

[0022] Figure 6 For the convergence graph of accuracy index when performing initial traffic flow assignment;

[0023] Figure 7 This is a diagram of the hybrid graph attention network structure.

[0024] Figure 8 The graph shows the decrease in the loss function during training.

[0025] Figure 9 A graph showing the accuracy metrics of a hybrid graph attention network;

[0026] Figure 10 This is a comparison of the computational efficiency of the hybrid graph attention network and the traditional Frank-Wolfe algorithm. Detailed Implementation

[0027] The technical solution of the present invention will be further described below with reference to the accompanying drawings, but it is not limited thereto. Any modifications or equivalent substitutions to the technical solution of the present invention that do not depart from the spirit and scope of the technical solution of the present invention should be covered within the protection scope of the present invention.

[0028] This invention provides a fast importance ranking method for large-scale urban bridge and tunnel networks based on hybrid graph attention networks, the method comprising the following steps:

[0029] Step 1: Define an individual importance index that considers the probability of structural failure and the economic losses incurred after failure in terms of safety, society, function, and environment.

[0030] The importance index of a single structural element can be calculated using the following formula:

[0031]

[0032] In the formula, Monomer structure Important indicators Monomer structure The probability of failure, Monomer structure The economic losses resulting from failure are expressed as the sum of economic losses incurred in the dimensions of safety, society, function, and environment. For economic losses in terms of security, As for economic losses in the social dimension, For economic losses in the functional dimension, Economic losses in the environmental dimension.

[0033] Economic losses in the security dimension It can be calculated using the following formula:

[0034]

[0035] In the formula, It consists of the cost of repairs required to address structural failure. The structural cost per unit area is $1294 / m² according to the AASHTO standard. 2 , and These represent the planar width and length (m) of the single-unit structure, respectively.

[0036] Social dimension economic loss It can be calculated using the following formula:

[0037]

[0038] In the formula, It consists of compensation for personal injuries or deaths caused by structural failure. For normal operation of single-unit structure The average daily traffic volume (veh / h) of the road in question. For traffic Time-monomer structure Traffic speed on the road (km / h) and The average number of passengers per passenger vehicle and freight vehicle is taken as 1.5 and 1.05 respectively, according to AASHTO standards. Monomer structure The proportion of trucks in the total traffic volume on the road is [missing information]. Regarding the standard for compensation for death, according to Article 15 of the "Interpretation of the Supreme People's Court on Several Issues Concerning the Application of Law in the Trial of Personal Injury Compensation Cases" (Death compensation shall be calculated based on the per capita disposable income of urban residents in the area where the court hearing the case is located in the previous year, calculated over a period of twenty years. However, for those over sixty years of age, the period shall be reduced by one year for each additional year of age; for those over seventy-five years of age, it shall be calculated over a period of five years), the per capita disposable income of urban residents in the area in the previous year shall be used. The corresponding value can be obtained by consulting the latest economic and social development statistical bulletin of the town where the bridge and tunnel network is located. The percentage of the population in the age group [i, i+1) can be obtained by consulting the latest census data of the towns where the bridge and tunnel network is located. Let i be the annual standard for population compensation for the age range [i, i+1), where i is the age.

[0039] Economic losses in functional dimensions It can be calculated using the following formula:

[0040]

[0041] In the formula, Additional detour time cost caused by structural failure ( and distance cost )composition, Monomer structure The number of detour days (d) resulting from a failure can be determined according to the relationship between detour days and traffic volume in the AASHTO standard. and These are the average unit time values ​​for passenger cars and freight cars, respectively, which are taken as $7.05 / h and $20.56 / h according to AASHTO standards. and These represent the average unit distance value for passenger cars and freight cars, respectively, which are set at $0.08 / km and $0.375 / km according to AASHTO standards. and They are monomer structures Before and after failure The average daily traffic volume (veh / h). For the edge The traffic is The passage time at that time For the edge Length (km) It is a bridge-tunnel network edge set.

[0042] Economic losses in environmental dimensions It can be calculated using the following formula:

[0043]

[0044] In the formula, Structural carbon emission costs resulting from structural failure ) and the additional carbon emission costs of detours ( )composition, and These are the market carbon price per unit (¥ / t) and the carbon emissions per unit area (g / m²). 2 Based on the carbon market trading price in my country as of the end of last year and the AASHTO regulations, the values ​​were 97.49 and 33600 respectively. and These are the average carbon emissions per unit distance for passenger cars and freight cars, respectively, which are taken as 161g / km and 604.9g / km according to AASHTO standards.

[0045] Step 2: Calculate the total trip volume, total arrival volume, and inter-node travel demand for each node in the bridge-tunnel network, where:

[0046] The total travel volume of each node in the bridge-tunnel network is calculated based on the resident population of its respective administrative region (county): the total travel volume of each node equals the total arrival volume, which is equal to the resident population of the administrative region (county) where the node is located divided by the number of nodes located in that administrative region (county). The travel demand between nodes is calculated using a gravity model, with the specific formula as follows:

[0047]

[0048] In the formula, For nodes and nodes The amount of attraction between them and They are nodes Total departures and nodes Total arrivals For nodes , Distance between (km) These are the hyperparameters of the gravity model. and To satisfy the constraint factors of travel and arrival constraints, the solution is obtained by alternately solving until... and The calculation can be stopped once the calculation error meets the set convergence threshold.

[0049] Step 3: Implement initial traffic flow assignment based on the Frank-Wolfe algorithm, where:

[0050] The optimization objective and constraint formulas for the initial traffic flow assignment are as follows:

[0051]

[0052] In the formula, Let the vector be composed of the flows of each edge. For path The above nodes , For the flow of traffic at origin and destination, For path set, The coefficient is 0-1, if the path Passing by If the value is 1, then the value is 1; otherwise, it is 0.

[0053] The main implementation process of the Frank-Wolfe algorithm is as follows:

[0054] Step 1, Initialization: Set the travel time of all edges to the travel time under free flow conditions, i.e. Based on this, an all-or-nothing (AON) allocation is performed to obtain the segment traffic. ,make ;

[0055] Step 2: Update travel times: Based on the initial data acquisition, substitute the BPR formula to update the travel times for each side, i.e. ;

[0056] Step 3: Determine the descent direction: after the update time Based on this, AON allocation is performed to obtain auxiliary traffic. The direction of descent is obtained by subtracting the traffic flow from the auxiliary traffic flow.

[0057] Step 4: Determine the iteration step size: Solve To obtain the optimal step size ;

[0058] Step 5, Move: Command ;

[0059] Step 6: Convergence test: If the convergence condition is met... ( If the preset accuracy index is not met, the algorithm terminates. That is, traffic flow, otherwise Then return to the second step of the calculation until the convergence condition is met.

[0060] Step 4: Disrupt potentially faulty edges in the bridge-tunnel network one by one to generate a dataset of traffic flow redistribution, where:

[0061] The dataset was created by progressively reducing the capacity of edges in the bridge-tunnel network that might fail (i.e., contain individual bridge-tunnel structures) using a random capacity reduction factor. The specific formula is as follows:

[0062]

[0063] In the formula, and The bridge and tunnel structures are respectively under normal operation and after failure. The capacity of the edge (veh / h). This represents the reduction factor. When creating the dataset, 40 failure scenarios were created for each edge containing a bridge / tunnel unit, and this was ensured... There are 10 operating conditions in each of the intervals [0.1, 0.3], [0.3, 0.5], [0.5, 0.7], and [0.7, 0.9].

[0064] Step 5: Design a hybrid graph attention network to model the topological association patterns between the edge capacity reduction vector and the flow redistribution vector in the bridge-tunnel network, where:

[0065] The hybrid graph attention network takes the edge capacity reduction coefficient vector of the bridge-tunnel network as input and the flow redistribution normalization vector of each edge as output. Its structure includes a node-edge feature transformation layer, a fully connected layer, and hybrid graph attention blocks (static attention layer and dynamic attention layer), specifically:

[0066] L0 layer: Node-edge feature transformation layer, input data scale is [value missing]. The two-dimensional data represent batches and edges respectively. This layer operates on the edge dimension and is related to the association matrix. Multiplying by the transpose of the expression converts edge information into node information, and the output data scale is [value missing]. , This represents the total number of nodes in the bridge-tunnel network.

[0067] L1 layer: Fully connected layer, connecting to L0 layer. This layer increases the dimensionality of the data to three dimensions. It adds a feature dimension after the batch and node dimensions, and then operates on the feature dimension. The input feature count is 1, and the output feature count is... The output data scale is ;

[0068] L2-1 layer: Static attention layer, following L1 layer. This layer operates on the spatial and feature dimensions, with an input feature count of... The number of output features is The output data scale is ;

[0069] L2-2 layer: Dynamic attention layer, following the L1 layer. This layer operates in both spatial and feature dimensions, with an input feature count of... The number of output features is The output data scale is ;

[0070] L3-1 layer: Static attention layer, following L1 layer. This layer operates in the spatial and feature dimensions, with an input feature count of... The number of output features is The output data scale is ;

[0071] L3-2 layer: Dynamic attention layer, following L1 layer. This layer operates in both spatial and feature dimensions, with an input feature count of... The number of output features is The output data scale is ;

[0072] L4 layer: A fully connected layer, connecting to layers L2-1, L2-2, L3-1, and L3-2. This layer first operates on the feature dimension, with the number of input features being... The output feature count is 1, and the data is then reduced to two dimensions, resulting in an output data scale of [size missing]. ;

[0073] Layer L5: Node-edge feature transformation layer, following layer L4. This layer operates at the node dimension and relates to the association matrix. Multiplication converts node information into edge information, and the output data scale is [size missing]. ;

[0074] Among them, layers L0 and L5 have no activation functions, while the activation functions of the remaining layers are all ReLU.

[0075] The formula for attention blocks in a hybrid graph is:

[0076]

[0077] In the formula, , These are the input and output of the l-th hybrid graph attention block, respectively. For multi-head attention operation, For graph convolution operations, and These are the adjacency matrix and the learnable adjacency matrix of the bridge-tunnel network, respectively. The former has fixed parameters, while the latter updates the element values ​​in the association matrix iteratively through the parameters. and For learnable embedding matrices, For the embedded dimension.

[0078] Step 6: Train the hybrid graph attention network designed in Step 5, and use the trained hybrid graph attention network to quickly rank the importance of large-scale urban bridge and tunnel networks.

[0079] Example 1

[0080] This embodiment provides a method for fast ranking of the importance of large-scale urban bridge and tunnel networks based on hybrid graph attention networks, such as... Figure 1 As shown, the method includes the following steps:

[0081] Step 1: Define an individual importance index that considers the probability of structural failure and the economic losses incurred after failure in terms of safety, society, function, and environment. The specific formula is as follows:

[0082]

[0083] In the formula, Monomer structure Important indicators Monomer structure The probability of failure, Monomer structure The economic losses resulting from failure are expressed as the sum of economic losses incurred in the dimensions of safety, society, function, and environment. Economic losses from a safety perspective consist of the repair costs required to address structural failures. The structural cost per unit area is $1294 / m² according to the AASHTO standard. 2 , and These represent the planar width and length (m) of the single-unit structure, respectively. Economic losses in the social dimension consist of compensation for personal injuries or deaths caused by structural failure. For normal operation of single-unit structure The average daily traffic volume (veh / h) of the road in question. For traffic Time-monomer structure Traffic speed on the road (km / h) and The average number of passengers per passenger vehicle and freight vehicle is taken as 1.5 and 1.05 respectively, according to AASHTO standards. Monomer structure The proportion of trucks in the total traffic volume on the road is [missing information]. Regarding the standard for compensation for death, according to Article 15 of the "Interpretation of the Supreme People's Court on Several Issues Concerning the Application of Law in the Trial of Personal Injury Compensation Cases" (Death compensation shall be calculated based on the per capita disposable income of urban residents in the area where the court hearing the case is located in the previous year, calculated over a period of twenty years. However, for those over sixty years of age, the period shall be reduced by one year for each additional year of age; for those over seventy-five years of age, it shall be calculated over a period of five years), the per capita disposable income of urban residents in the area in the previous year shall be used. The corresponding value can be obtained by consulting the latest economic and social development statistical bulletin of the town where the bridge and tunnel network is located. The percentage of the population in the age group [i, i+1) can be obtained by consulting the latest census data of the towns where the bridge and tunnel network is located. The annual standard for population compensation is for the age group [i, i+1). The economic loss in terms of functionality is the additional detour time cost caused by structural failure. and distance cost )composition, Monomer structure The number of detour days (d) resulting from a failure can be determined according to the relationship between detour days and traffic volume in the AASHTO standard. and These are the average unit time values ​​for passenger cars and freight cars, respectively, which are taken as $7.05 / h and $20.56 / h according to AASHTO standards. and These represent the average unit distance value for passenger cars and freight cars, respectively, which are set at $0.08 / km and $0.375 / km according to AASHTO standards. and They are monomer structures Before and after failure The average daily traffic volume (veh / h). For the edge The traffic is The passage time at that time For the edge Length (km) For bridge and tunnel network edge sets, The environmental economic loss is the structural carbon emission cost caused by structural failure. ) and the additional carbon emission costs of detours ( )composition, and These are the market carbon price per unit (¥ / t) and the carbon emissions per unit area (g / m²). 2 Based on the carbon market trading price in my country as of the end of last year and the AASHTO regulations, the values ​​were 97.49 and 33600 respectively. and These are the average carbon emissions per unit distance for passenger cars and freight cars, respectively, which are taken as 161g / km and 604.9g / km according to AASHTO standards.

[0084] Step 2: Calculate the total number of trips, total number of arrivals, and travel demand between nodes in the bridge-tunnel network.

[0085] Taking Wuhan's bridge and tunnel network (including 462 nodes, 815 edges, and 681 individual bridge and tunnel structures) as an example, such as Figure 2 As shown. The total travel volume of each node in the bridge-tunnel network is calculated based on the resident population of its respective administrative region (county): the total travel volume of each node equals the total arrival volume, which is equal to the resident population of the administrative region (county) where the node is located divided by the number of nodes located in that administrative region (county). The attraction between nodes is calculated based on the gravity model, with the specific formula as follows:

[0086]

[0087] In the formula, For nodes and nodes The amount of attraction between them and They are nodes Total departures and nodes Total arrivals For nodes , Distance between (km) The hyperparameter of the gravity model is set to 0.05. and To satisfy the constraint factors of travel and arrival constraints, the solution is obtained by alternately solving until... and The calculation stops when the calculation error meets the set convergence threshold. In this embodiment, the convergence threshold is set to 1E-8, and the calculation error convergence is as follows. Figure 3 As shown, the calculated inter-node travel demand matrix is ​​as follows: Figure 4 As shown.

[0088] Step 3: Implement initial traffic flow assignment based on the Frank-Wolfe algorithm. The optimization objective and constraint formulas for the initial traffic flow assignment are as follows:

[0089]

[0090] In the formula, Let the vector be composed of the flows of each edge. For path The above nodes , For the flow of traffic at origin and destination, For path set, The coefficient is 0-1, if the path Passing by If the value is 1, then the value is 1; otherwise, it is 0.

[0091] The main implementation process of the Frank-Wolfe algorithm is as follows: Step 1 (Initialization): Set the travel time of all edges to the travel time under free flow conditions, i.e. Based on this, perform the All-or-Nothing (AON) allocation to obtain the segment traffic. ,make Step 2 (Update Travel Time): Based on the initial data acquisition, the travel time for each side is updated using the BPR formula, i.e. Step 3 (Determine the descent direction): After the update time ( Based on this, AON allocation is performed to obtain auxiliary traffic. The fourth step (determining the iteration step size) involves subtracting the road segment flow from the auxiliary flow to obtain the descent direction. Obtain the optimal step size Step 5 (Move): Command Step 6 (Convergence Test): If the convergence condition is met... ( If the preset accuracy index is not met, the algorithm terminates. That is, traffic flow, otherwise Then return to step two for calculation until the convergence condition is met. This embodiment takes... For 1E-5, the objective function descent plot and accuracy index The convergence plots are as follows: Figure 5 and Figure 6 As shown.

[0092] Step 4: Destroy potentially faulty edges in the bridge-tunnel network one by one to generate a dataset of traffic flow redistribution.

[0093] The dataset was created by progressively reducing the capacity of edges in the bridge-tunnel network that might fail (i.e., contain individual bridge-tunnel structures) using a random capacity reduction factor. The specific formula is as follows:

[0094]

[0095] In the formula, and The bridge and tunnel structures are respectively under normal operation and after failure. The capacity of the edge (veh / h). This represents the reduction factor. When creating the dataset, 40 failure scenarios were created for each edge containing a bridge / tunnel unit, and this was ensured... There are 10 operating conditions in each of the intervals [0.1, 0.3], [0.3, 0.5], [0.5, 0.7], and [0.7, 0.9].

[0096] Step 5: Design a hybrid graph attention network to model the topological relationship between the edge capacity reduction coefficient and the flow redistribution solution of the bridge-tunnel network.

[0097] The hybrid graph attention network takes the capacity reduction coefficient vector of the bridge-tunnel network edge as input and the normalized vector of flow redistribution of each edge as output. Its structure includes a node-edge feature transformation layer, a fully connected layer, and hybrid graph attention blocks (static attention layer and dynamic attention layer), such as... Figure 7 As shown, specifically:

[0098] L0 (Node-Edge Feature Transformation) layer: Input data scale is The two-dimensional data represent batches and edges respectively. This layer operates on the edge dimension and is related to the association matrix. Multiplying by the transpose of the expression converts edge information into node information, and the output data scale is [value missing]. ;

[0099] L1 (Fully Connected) Layer: Following L0, this layer increases the data dimensionality to three dimensions. It adds a feature dimension after the batch and node dimensions, and then operates on the feature dimension. The input feature count is 1, and the output feature count is [missing value]. The output data scale is ;

[0100] L2-1 (Static Attention) Layer: Following the L1 layer, this layer operates on the spatial and feature dimensions, with an input feature count of... The number of output features is The output data scale is ;

[0101] L2-2 (Dynamic Attention) Layer: Following the L1 layer, this layer operates on the spatial and feature dimensions, with an input feature count of... The number of output features is The output data scale is ;

[0102] L3-1 (Static Attention) Layer: Following the L1 layer, this layer operates on the spatial and feature dimensions, with an input feature count of... The number of output features is The output data scale is ;

[0103] L3-2 (Dynamic Attention) Layer: Following the L1 layer, this layer operates on the spatial and feature dimensions, with an input feature count of... The number of output features is The output data scale is ;

[0104] L4 (fully connected) layer: Connects to L2-1, L2-2, L3-1, and L3-2 layers. This layer first operates on the feature dimension, with the input feature number being... The output feature count is 1, and the data is then reduced to two dimensions, resulting in an output data scale of [size missing]. ;

[0105] L5 (Node-Edge Feature Transformation) layer: Following the L4 layer, this layer operates at the node dimension and interacts with the association matrix. Multiplication converts node information into edge information, and the output data scale is [size missing]. ;

[0106] In this layer, layers L0 and L5 have no activation function, while the activation function for all other layers is ReLU.

[0107] The formula for attention blocks in a hybrid graph is:

[0108]

[0109] In the formula, respectively For the input and output of the l-th hybrid graph attention block, For multi-head attention operations, the number of attention heads is set to 8. For graph convolution operations, and These are the adjacency matrix and the learnable adjacency matrix of the bridge-tunnel network, respectively. The former has fixed parameters, while the latter updates the element values ​​in the association matrix iteratively through the parameters. and For learnable embedding matrices, The embedding dimension is set to 32.

[0110] Step Six: Use the bridge and tunnel network of Wuhan as a case study to train and test the model.

[0111] After redistribution, the flow is standardized along edges to [0, 1], scaling the flow of each edge to a uniform scale under each working condition. The loss function is the MSE function, the training epochs are set to 100, the optimization method is the Adam method, the learning rate is set to 0.001, and RMSE, MAE, and R are selected. 2 As a metric for evaluating the accuracy of hybrid graph attention networks, the loss function decreases during model training as shown in the graph. Figure 8 As shown, the error decreases rapidly in the first 10 training rounds and then smoothly converges to 0.014 in the subsequent rounds. Figure 9 The accuracy metrics of the hybrid graph attention network on the training, validation, and test sets are presented. It can be seen that R... 2 The values ​​are consistently greater than 0.95, and the RMSE and MAE values ​​are very close. Furthermore, the values ​​of these three indicators remain stable without any sudden changes, indicating that the proposed hybrid graph attention network model can accurately provide traffic flow redistribution results under various capacity reduction scenarios without underfitting or overfitting issues. Figure 10 This paper presents a comparison of the efficiency of the proposed hybrid graph attention network and the traditional Frank-Wolfe algorithm in calculating traffic flow redistribution results for bridge and tunnel networks in Wuhan. The traditional Frank-Wolfe algorithm requires repeated solutions to high-dimensional traffic flow redistribution when calculating large-scale bridge and tunnel networks, with a total computation time exceeding one day. In contrast, the trained hybrid graph attention network can complete batch calculations in less than one minute, achieving a computational efficiency advantage of at least four orders of magnitude. This enables accurate and rapid calculation of importance indicators for large-scale urban bridge and tunnel networks.

Claims

1. A method for fast ranking of the importance of large-scale urban bridge and tunnel networks based on hybrid graph attention networks, characterized in that... The method includes the following steps: Step 1: Define an individual importance index that considers the probability of structural failure and the economic losses that will result in safety, society, function, and environment after failure. Step 2: Calculate the total number of trips, total number of arrivals, and travel demand between nodes in the bridge-tunnel network; Step 3: Implement initial traffic flow assignment based on the Frank-Wolfe algorithm; Step 4: Destroy potentially faulty edges in the bridge-tunnel network one by one to generate a dataset of traffic flow redistribution; Step 5: Design a hybrid graph attention network to model the topological association patterns between the edge capacity reduction vector and the flow redistribution vector in the bridge-tunnel network; Step 6: Train the hybrid graph attention network designed in Step 5, and use the trained hybrid graph attention network to quickly rank the importance of large-scale urban bridge and tunnel networks.

2. The method for fast ranking of importance of large-scale urban bridge and tunnel networks based on hybrid graph attention networks according to claim 1, characterized in that... The importance index of the single-unit structure is calculated by the following formula: In the formula, Monomer structure Important indicators Monomer structure The probability of failure, Monomer structure Economic losses resulting from failure For economic losses in terms of security, As for economic losses in the social dimension, For economic losses in the functional dimension, Economic losses in the environmental dimension.

3. The method for fast ranking of importance of large-scale urban bridge and tunnel networks based on hybrid graph attention networks according to claim 2, characterized in that... The economic losses in the security dimension Calculated by the following formula: In the formula, Cost per unit area of ​​structure and These are the planar width and length of the single-unit structure, respectively. The social dimension of economic loss Calculated by the following formula: In the formula, For normal operation of single-unit structure The average daily traffic volume of the road in question. For traffic Time-monomer structure The traffic speed on the road in question and The average number of passengers per passenger vehicle and freight vehicle. Monomer structure The proportion of trucks in the total traffic volume on the road is [missing information]. The standard for compensation for death. This represents the proportion of the population in the age group [i, i+1). Let i be the annual standard for population compensation for the age range [i, i+1), where i is the age in years. Economic losses in the functional dimensions Calculated by the following formula: In the formula, To incur additional detour time costs, For distance cost, Monomer structure The number of detour days caused by the failure and These represent the average unit time value for passenger cars and freight cars, respectively. and These represent the average unit distance value for passenger cars and freight cars, respectively. and They are monomer structures Before and after failure The average daily traffic volume For the edge The traffic is The passage time at that time For the edge Length, For bridge and tunnel network edge sets; The economic losses in the environmental dimension Calculated by the following formula: In the formula, For the cost of structural carbon emissions, To incur additional carbon emission costs associated with bypassing carbon emission pathways, and These are the market carbon price and the carbon emissions per unit area, respectively. and These represent the average carbon emissions per unit distance for passenger cars and freight cars, respectively.

4. The method for fast ranking of importance of large-scale urban bridge and tunnel networks based on hybrid graph attention networks according to claim 1, characterized in that... In step two, the total travel volume of each node in the bridge-tunnel network is calculated based on the resident population of its respective administrative region (county): the total travel volume of each node equals the total arrival volume, which is equal to the resident population of the administrative region (county) where the node is located divided by the number of nodes located in that administrative region (county). The travel demand between nodes is calculated based on the gravity model, and the specific formula is as follows: In the formula, For nodes and nodes The amount of attraction between them and They are nodes Total departures and nodes Total arrivals For nodes , The distance between them These are the hyperparameters of the gravity model. and Constraint factors that satisfy travel and arrival constraints.

5. The method for fast ranking of importance of large-scale urban bridge and tunnel networks based on hybrid graph attention networks according to claim 3, characterized in that... In step three, the optimization objective and constraint formulas for the initial traffic flow assignment are as follows: In the formula, Let the vector be composed of the flows of each edge. For path The above nodes , For the flow of traffic at origin and destination, For path set, The coefficient is 0-1, if the path Passing by If the value is 1, then the value is 1; otherwise, it is 0.

6. The method for fast ranking of importance of large-scale urban bridge and tunnel networks based on hybrid graph attention networks according to claim 1, characterized in that... In step three, the main implementation process of the Frank-Wolfe algorithm is as follows: Step 1, Initialization: Set the travel time of all edges to the travel time under free flow conditions, i.e. Based on this, an all-in-one (AON) allocation is performed to obtain the segment traffic. ,make ; Step 2: Update travel times: Based on the initial data acquisition, substitute the BPR formula to update the travel times for each side, i.e. ; Step 3: Determine the descent direction: after the update time Based on this, AON allocation is performed to obtain auxiliary traffic. The direction of descent is obtained by subtracting the traffic flow from the auxiliary traffic flow. Step 4: Determine the iteration step size: Solve To obtain the optimal step size ; Step 5, Move: Command ; Step 6: Convergence test: If the convergence condition is met... , If the preset accuracy target is not met, the algorithm terminates. That is, traffic flow, otherwise Then return to the second step of the calculation until the convergence condition is met.

7. The method for fast ranking of importance of large-scale urban bridge and tunnel networks based on hybrid graph attention networks according to claim 1, characterized in that... In step four, the dataset is created by gradually reducing the capacity of potentially failing edges in the bridge-tunnel network using a random capacity reduction factor. The specific formula is as follows: In the formula, and The bridge and tunnel structures are respectively under normal operation and after failure. The capacity of the edge is This is the reduction factor.

8. The method for fast ranking of importance of large-scale urban bridge and tunnel networks based on hybrid graph attention networks according to claim 1, characterized in that... In step four, the hybrid graph attention network takes the bridge-tunnel network edge capacity reduction coefficient vector as input and the flow redistribution normalization vector of each edge as output. Its structure includes a node-edge feature transformation layer, a fully connected layer, and a hybrid graph attention block, specifically: L0 layer: Node-edge feature transformation layer, input data scale is [value missing]. The two-dimensional data represent batches and edges respectively. This layer operates on the edge dimension and is related to the association matrix. Multiplying by the transpose of the expression converts edge information into node information, and the output data scale is [value missing]. , This represents the total number of nodes in the bridge-tunnel network. L1 layer: Fully connected layer, connecting to L0 layer. This layer increases the dimensionality of the data to three dimensions. It adds a feature dimension after the batch and node dimensions, and then operates on the feature dimension. The input feature count is 1, and the output feature count is... The output data scale is ; L2-1 layer: Static attention layer, following L1 layer. This layer operates on the spatial and feature dimensions, with an input feature count of... The number of output features is The output data scale is ; L2-2 layer: Dynamic attention layer, following the L1 layer. This layer operates in both spatial and feature dimensions, with an input feature count of... The number of output features is The output data scale is ; L3-1 layer: Static attention layer, following L1 layer. This layer operates in the spatial and feature dimensions, with an input feature count of... The number of output features is The output data scale is ; L3-2 layer: Dynamic attention layer, following L1 layer. This layer operates in both spatial and feature dimensions, with an input feature count of... The number of output features is The output data scale is ; L4 layer: A fully connected layer, connecting to layers L2-1, L2-2, L3-1, and L3-2. This layer first operates on the feature dimension, with the number of input features being... The output feature count is 1, and the data is then reduced to two dimensions, resulting in an output data scale of [size missing]. ; Layer L5: Node-edge feature transformation layer, following layer L4. This layer operates at the node dimension and relates to the association matrix. Multiplication converts node information into edge information, and the output data scale is [size missing]. ; Among them, layers L0 and L5 have no activation functions, while the activation functions of the remaining layers are all ReLU.

9. The method for fast ranking of importance of large-scale urban bridge and tunnel networks based on hybrid graph attention networks according to claim 8, characterized in that... The formula for the attention block in the hybrid graph is: In the formula, , These are the input and output of the l-th hybrid graph attention block, respectively. For multi-head attention operation, For graph convolution operations, and These are the adjacency matrix and the learnable adjacency matrix of the bridge-tunnel network, respectively. and is a learnable embedding matrix.

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